Self-Consistency Aspects of Dielectric Mixing Theories

摘要

Dielectric mixing formulas are considered that relate the effective permittivity of a heterogenous medium with the properties of the constituent materials. The restriction for this approach is that the sizes of the inclusions in the mixture have to be considerably smaller than the wavelength in order to avoid scattering effects. The mixing rules are presented for cases where the scatterers can be homogeneous or multilayer spheres. The formula contains a free parameter upsilon and for different choices of this parameter, many mixing formulas result as special cases of the given mixing rule. For the case of one-dimensional spheres, the value upsilon = 0 is shown to yield the correct mixing formula. However, in three dimensions, the situation may be different because no exact solution for the problem with random geometries exists. Mixing formulas presented in the literature are also reviewed and the results from different formulas are compared, using dry snow as a paradigmatic example.